Normalized Pressure Gradient Research Articles

Influence of lower hybrid wave injection on peeling-ballooning modes

The high-confinement mode (H-mode) significantly enhances the energy and particle confinement in fusion plasma compared with the low-confinement mode (L-mode), and it is the basic operation scenario for ITER and CFETR. Edge localized mode (ELM) often appears in H-mode, helping to expel impurities to maintain a longer stable state. However, the particle burst and energy burst from ELM eruptions can severely damage the first wall of fusion device, so, it is necessary to control the ELM. Experiments on EAST tokamak and HL-2A tokamak have been conducted with ELM mitigation by lower hybrid wave (LHW), confirming the effect of LHW on ELMs, but the physical mechanism of ELM mitigation by LHW is still not fully understood. In this paper, the influences of LHW injection on the linear and nonlinear characteristics of peeling-ballooning mode (P-B mode) are investigated in the edge pedestal region of H-mode plasma in tokamak by using the BOUT++ code. The simulations take into consideration both the conventional main plasma current driven by LHW and the three-dimensional perturbed magnetic field generated by the scrape-off layer helical current filament (HCF) on the P-B mode. The linear results show that the core plasma current driven by LHW moves the linear toroidal mode spectrum towards higher mode numbers and lower growth rates by reducing the normalized pressure gradient and magnetic shear of the equilibrium. Nonlinear simulations indicate that due to the broadening of the linear mode spectrum, the core current driven by LHW can reduce the pedestal energy loss caused by ELM through globally suppressing different toroidal modes of the P-B mode, and the three-dimensional perturbed magnetic field generated by LHW-driven HCF can reduce the energy loss caused by ELMs through promoting the growth of modes other than the main mode and enhancing the coupling between different modes. It is found in the study that the P-B mode promoted by the three-dimensional perturbed magnetic field generated by HCF has a mode number threshold, and when the dominant mode of the P-B mode is far from the mode number threshold driven by the three-dimensional perturbed magnetic field, the energy loss due to ELMs is more significantly reduced. These results contribute to a more in-depth understanding of the physical mechanism in ELM control experiment by LHW.

MHD effects of liquid metal flows through multiple electrically coupling ducts with U-turn bends in fusion blankets

The investigation of liquid metal (LM) magnetohydrodynamic (MHD) flows through multiple electrically coupling ducts with U-turn bends is of crucial importance for accurately predicting the thermal-hydraulic performance of LM blankets in fusion reactors. Moreover, this duct configuration is often adopted in liquid blanket designs. Here, the combination effects of the MHD coupling, 3D MHD and inclined external magnetic fields on LM MHD flows through the multiple coupling ducts with different aspect ratios and wall conductance ratios are systematically investigated by numerical simulations. The results indicate that the MHD pressure gradient caused by MHD coupling effect decreases but the 3D MHD pressure gradient increases firstly and then decreases as the inclined angles of external magnetic fields increase. In addition, the results also indicate that the normalized pressure gradient can be reduced by increasing the wall conductance ratio () through the increase of the wall thickness. Furthermore, an important finding is that the pressure gradients caused by the MHD coupling decrease with the increases of aspect ratios (b/a) of ducts, while the 3D MHD pressure gradient when b/a = 16 increases to an excessive large degree about 40 times of the pressure gradient in a single conductive duct. The related investigation results will provide a theoretical support for the liquid blanket designs in fusion reactors and deepen our understanding on the LM MHD effects.

Study on divertor detachment and pedestal characteristics in the DIII-D upper closed divertor

Experiments performed in DIII-D demonstrate that higher plasma current and heating power combined with impurity seeding facilitate the achievement of divertor detachment with a higher pedestal pressure and higher plasma performance in H-mode plasmas with a baffled closed divertor compared with an open divertor. Dedicated experiments were carried out to study the impact of power, plasma current and impurity seeding on divertor detachment with ion directed into the divertor favorable for the L–H transition. With a factor of three variation in heating power and with only D2 puffing, no significant difference in the separatrix density at detachment onset was found. The higher heating power leads to higher impurity concentration and wider scrape-off layer (SOL) width, and reduces the detachment onset density to one similar to that in lower-power plasmas. Higher current requires higher pedestal and line-averaged densities to achieve divertor detachment; however, the increase in separatrix density at increasing plasma current is found to be less pronounced. Initial calculations found that both power scan and plasma current scan datasets are qualitatively consistent with theory after considering the change in impurity concentration and heat flux width. This also motivates the future extensive study of transport and divertor impurity behavior in order to have a quantitative comparison between experiment and theory. Compared with an open divertor, a closed divertor facilitates detachment onset at ∼40% lower line-averaged plasma density. Additional N2 seeding facilitates the achievement of detachment at a lower separatrix density and thus a higher pedestal temperature, which is beneficial for advanced tokamak scenarios. Higher heating power requires a higher N2 puffing rate to achieve the same degree of detachment, while a higher N2 puffing rate leads to lower detachment onset line-averaged density, both of which agree with theory. In contrast to the narrower pedestal in an open divertor approaching detachment, the pedestal density width in a closed divertor increases with density. The density gradient increases with line-averaged density at higher plasma current, but remains nearly unchanged at lower plasma current. In particular, compared with discharges with low power, at high heating power the pedestal density gradient is much weaker, while the SOL density is significantly higher and wider. At the same plasma current, both pedestal pressure gradient and temperature gradient decrease linearly with the line-averaged density but remain similar across different heating powers. Even with different plasma current and heating power, the normalized pressure gradient remains identical. As a result, achievement of divertor detachment with a higher pedestal pressure and higher plasma performance is shown in a closed divertor, which is important for improving core–edge integration as one of the critical issues for future tokamak fusion reactors.

Destabilization of low-frequency modes (LFMs) driven by a thermal pressure gradient in EAST plasmas with q min ⩽ 2

Mode structures and excitation conditions for the low-frequency modes (LFMs) have been investigated in experimental advanced superconducting tokamak (EAST) plasmas with q min ⩽ 2. Two different stages/categories of the LFM instabilities are observed during the oscillation of annular/central collapse events: (I) the upward sweeping frequency of LFMs; (II) the upward frequency jumpsof LFMs. The annular/central events are triggered by the m/n = 2/1 double tearing modes with different q-profiles, while the LFMs are characterized by higher mode numbers m/n = 4/2, 6/3, …, where m and n are the poloidal and toroidal mode numbers, respectively. The maximum radial coverage of the LFMs is located in the annular region of 1.97 2.07 m with the normalized minor radius 0.2 0.4, while the higher-frequency (or upward sweeping frequency) branch is more localized to the radial position of 2 2.02 m (q min). The frequency characteristics of upward sweeps or upward jumps of the LFMs are mainly attributed to the change in the q-profile, e.g. the upward sweeping frequency in stage I is caused by q min decreasing. Accordingly, the linear wave properties of LFMs in EAST with weak/reversed magnetic shear are studied numerically and analytically based on a general fishbone-like dispersion relation. Without considering the contribution of energetic ions, it is shown that the LFM with Alfvénic polarization is an MHD-unstable kinetic ballooning mode with frequency of the order of the ion diamagnetic drift frequency. Several important factors for the excitation of LFM instability are analyzed: (1) the role of energetic ions is unimportant, and the LFMs can be excited under the two conditions of with/without energetic ions; (2) the higher τ = T e/T i with larger η i = L ni /L Ti are required, namely the normalized pressure gradient α ∝ (1 + τ)(1 + η i) should be large enough to overcome the stability effect of finite field line bending; (3) the weak/reversed shear q-profile with q min ⩽ 2 and suitable S ≡ (r/q)(q″)1/2 are required.

Turbulent broadening of electron heat-flux width in electromagnetic gyrokinetic simulations of a helical scrape-off layer model

We demonstrate that cross field transport in the scrape-off layer (SOL) can be moderately increased by electromagnetic effects in high-beta regimes, resulting in broadening of the electron heat-flux width on the endplates. This conclusion is taken from full-f electromagnetic gyrokinetic simulations of a helical SOL model that roughly approximates the SOL of the National Spherical Torus Experiment. The simulations have been performed with the Gkeyll code, which recently became the first code to demonstrate the capability to simulate electromagnetic gyrokinetic turbulence on open magnetic field lines with sheath boundary conditions. We scan the source rate and thus β, so that the normalized pressure gradient (the MHD ballooning parameter α∝∂β/∂r∝β/Lp) is scanned over an experimentally relevant range, α=0.3−1.5. While there is little change in the pressure gradient scale length Lp near the midplane as beta is increased, a 10% increase in cross field transport near the midplane results in an increase in the electron heat-flux width λq and a 25% reduction of the peak electron heat flux to the endplates.

Influence of plasma shaping effect on peeling-ballooning instability

The influence of plasma shaping effect on peeling-ballooning mode is studied linearly and nonlinearly using the three-field module of BOUT++. Without considering the variations of pressure pedestal and bootstrap current induced by shaping, our simulations demonstrate that shaping effect on magnetic surfaces also influences peeling-ballooning instability significantly. The shape of growth rate spectrum tends to shift to a lower toroidal mode number () with the increase of elongation (), and the growth rates become smaller for all modes with the increase of triangularity () in the linear simulation. Further analysis demonstrates that peeling-ballooning mode is stabilized mainly by the increased magnetic shear () for elongation and the decreased normalized pressure gradient () for triangularity. In the nonlinear simulation, the elongation can lead to a larger pedestal collapse while the triangularity plays an opposing role. That is because the dominance of low mode that arises with the increase of and decrease of can lead to a larger energy loss. The results indicate that the effect of triangularity on the magnetic surface is quite important since it leads to ELM mitigation without any variations of pressure pedetal and bootstrap current, which provide an innovative mechanism to explain the ELM mitigation phenomenon due to plasma shaping.

Neural network surrogate of QuaLiKiz using JET experimental data to populate training space

Within integrated tokamak plasma modeling, turbulent transport codes are typically the computational bottleneck limiting their routine use outside of post-discharge analysis. Neural network (NN) surrogates have been used to accelerate these calculations while retaining the desired accuracy of the physics-based models. This paper extends a previous NN model, known as QLKNN-hyper-10D, by incorporating the impact of impurities, plasma rotation, and magnetic equilibrium effects. This is achieved by adding a light impurity fractional density (nimp,light/ne) and its normalized gradient, the normalized pressure gradient (α), the toroidal Mach number (Mtor), and the normalized toroidal flow velocity gradient. The input space was sampled based on experimental data from the JET tokamak to avoid the curse of dimensionality. The resulting networks, named QLKNN-jetexp-15D, show good agreement with the original QuaLiKiz model, both by comparing individual transport quantity predictions and by comparing its impact within the integrated model, JINTRAC. The profile-averaged RMS of the integrated modeling simulations is <10% for each of the five scenarios tested. This is non-trivial given the potential numerical instabilities present within the highly nonlinear system of equations governing plasma transport, especially considering the novel addition of momentum flux predictions to the model proposed here. An evaluation of all 25 NN output quantities at one radial location takes ∼0.1 ms, 104 times faster than the original QuaLiKiz model. Within the JINTRAC integrated modeling tests performed in this study, using QLKNN-jetexp-15D resulted in a speed increase of only 60–100 as other physics modules outside of turbulent transport become the bottleneck.

The unstable ELM evolution modulated by lower hybrid waves on EAST

Modulated lower hybrid waves, are injected into the Experimental Advanced Superconducting Tokamak (EAST), to investigate the modulated evolutions of pedestal structure and unstable edge-localized modes (ELMs). The spectrum patterns of show that the ELM amplitude only slightly decreases while the ELM frequency becomes almost 3–5 times larger as the lower hybrid radio frequency (LHRF) jumps into the lower power level. Pedestal structure analysis indicates that higher LHRF power injection can increase the plasma stored energy and core plasma parameters, accompanying with the pedestal shift and gradient increase. Ion saturation contour current plots suggest that LHRF power can deposit in the plasma edge region to profoundly change the three-dimensional (3D) magnetic topology, similarly to the effect of resonant magnetic perturbations (RMPs), by inducing the helical current filaments (HCFs) following along the magnetic field lines in the scrape-off layer (SOL), which may cause the density pump-out effect by increasing the radial plasma transport. The modulated higher temperature and lower density of pedestal top-values can reduce the pedestal collisionality, which will strongly increase the bootstrap current density and gradually shift the Peeling-Ballooning mode (PBM) boundary. ELITE code stability analysis indicates that LHRF injection can lead to the relatively unstable ELMs with a higher pedestal gradient, simultaneously accompanying with the normalized pressure gradient and edge bootstrap current density increase. All of these results imply that there is a significant correlation between the ELM behavior and pedestal structure modulation because of LHRF dissipation at the plasma edge for the unstable ELM modulated case.

Effect of pressure gradient in the connection region on the stability of the edge pedestal

We have numerically investigated the dependence of pedestal properties such as the pedestal height and the pedestal width on the normalized pressure gradient () in the connection region, . We used an ideal MHD stability code, MISHKA, and the pedestal predictive model, EPED1, to analyze the effect of on the edge stability and predict pedestal structure. Edge stability is affected by because the unstable mode extends radially into the core. Improvement of pedestal properties can be achieved by reducing . Effect of on the edge instability is largest for the intermediate mode n. Larger gradient of Shafranov shift, , also improves the pedestal width and height by stabilizing peeling-ballooning mode (PBM). Our result has been applied to JET hybrid discharges to explain the coupling between core and edge pressure profile in H-mode plasma configuration through and . The extended correlation loop between poloidal beta and the pedestal parameters is presented.

Feedback and Ballooning Instabilities in the Magnetosphere‐Ionosphere Coupling

AbstractA unified model for the feedback and ballooning instabilities in the magnetosphere‐ionosphere (M‐I) coupling is developed by means of the reduced magnetohydrodynamic and two‐fluid equations, involving the local current closure and the ionospheric conductivity change in a scale of auroral fine structures, self‐consistently. In a low pressure gradient case, the Alfvén harmonics are destabilized through the feedback mechanism, while the ballooning instability appears if the magnetospheric pressure gradient exceeds a critical value. Transition of the dominant instability between the feedback and ballooning modes is brought by change of the normalized pressure gradient or the convection electric field in the magnetosphere. The obtained results imply a variety of appearance of auroral arcs and beads in the M‐I coupling system.

Synergistic Effect between Surfactant and Nanoparticles on the Stability of Foam in EOR Processes

Summary The major challenge in enhanced oil recovery (EOR) by gas injection is poor volumetric sweep efficiency, mainly due to the high gas mobility and reservoir heterogeneity. Injecting gas as a foam increases sweep efficiency, but maintaining foam stability within the reservoir remains a challenge. This research evaluates the synergistic interaction of one type of nanoparticle and a surfactant to increase foam stability, using the concentration ratio of the two components to tune the affinity of the nanoparticle for the gas/liquid interface. We test the capability of the synergistic two-component system to stabilize methane foam and compare it with foam stabilized by surfactants only. A key distinction is the foam stability upon contact with oil, and we explain the observations in static and dynamic conditions. Foam stability was measured in both static (bubble structure) and dynamic (flow through porous media) conditions. In the static test, foam is generated by the shaking method, and foam texture (bubble size and shape) and the decay of foam height with time are indicators of foam stability. To test static stability in the presence of oil, heavy oil is injected into the foam/liquid interface. In dynamic tests, foam is pregenerated before flowing at elevated pressures into sandpacks containing various oil saturations. Normalized pressure gradient and apparent viscosity are the indicators of foam stability and effectiveness for improving oil recovery. The extent to which nanoparticles are covered with surfactant governs the foam stability, in both static and dynamic conditions. Static foam is stable in the presence of oil only if the nanoparticles are partially covered by the surfactant. In the dynamic test, foam stabilized with only the surfactant collapses in the porous media when oil is present. Nanoparticles alone could not generate foam regardless of the presence of oil or salinity, but foam stabilized with nanoparticles partially covered by surfactant is stable in the presence of both residual and initial oil, and foam apparent viscosity could reach up to 400 cp at residual heavy oil condition. In both static and dynamic conditions, nanoparticles completely covered with a bilayer of surfactant do not stabilize foam in the presence of oil. Partially covered nanoparticle foam also demonstrated salt tolerance in both static and dynamic tests, and foam apparent viscosity can reach up to 200 cp with high salinity and residual heavy oil presented. Thus, at appropriate surface coverage, the combination of nanoparticles and surfactant is more effective than either stabilizer alone. The result shows that interaction of surfactant and nanoparticles is important in foam stability in the porous media with oil. In particular, this interaction is synergistic at certain coverage. This type of synergy can provide much more robust mobility control for EOR processes involving gas injection.

Role of Microtearing Turbulence in DIII-D High Bootstrap Current Fraction Plasmas.

We report on the first direct comparisons of microtearing turbulence simulations to experimental measurements in a representative high bootstrap current fraction (f_{BS}) plasma. Previous studies of high f_{BS} plasmas carried out in DIII-D with large radius internal transport barriers (ITBs) have found that, while the ion energy transport is accurately reproduced by neoclassical theory, the electron transport remains anomalous and not well described by existing quasilinear transport models. A key feature of these plasmas is the large value of the normalized pressure gradient, which is shown to completely stabilize conventional drift-wave and kinetic ballooning mode instabilities in the ITB, but destabilizes the microtearing mode. Nonlinear gyrokinetic simulations of the ITB region performed with the cgyro code demonstrate that the microtearing modes are robustly unstable and capable of driving electron energy transport levels comparable to experimental levels for input parameters consistent with the experimental measurements. These simulations uniformly predict that the microtearing mode fluctuation and flux spectra extend to significantly shorter wavelengths than the range of linear instability, representing significantly different nonlinear dynamics and saturation mechanisms than conventional drift-wave turbulence, which is also consistent with the fundamental tearing nature of the instability. The predicted transport levels are found to be most sensitive to the magnetic shear, rather than the temperature gradients more typically identified as driving turbulent plasma transport.

Fluid flow, heat transfer and entropy generation analyses of turbulent forced convection through isotropic porous media using RANS models

Abstract Turbulent fluid flow, heat transfer and entropy generation through isotropic porous media were investigated utilizing two RANS models, i.e., RNG k - e and SST k - ω . Circular, longitudinal elliptical and transverse elliptical cross-sectional configurations were analyzed with symmetrical boundary conditions for the upper and lower lines and periodic boundary conditions for the back and front lines. Evaluation of the temperature contours indicated two low-temperature regions behind the solid rods of the transverse elliptical cross-sectional configuration exist. For a given specific normalized pressure gradient, dimensionless turbulence kinetic energy, Nusselt number, and heat transfer efficiency, the RNG k - e model resulted in more reliable results for the dimensionless turbulence kinetic energy at low Reynolds numbers when compared with the SST k - ω model. Using the thermal analysis of the three cross-sectional configurations investigated, the longitudinal elliptical resulted in higher heat transfer efficiencies when compared with the circular and transverse elliptical cross-sectional configurations. When the influence of the turbulence effects were included in the entropy generation rate, a second law of thermodynamics analysis indicated that the longitudinal elliptical cross-sectional configuration resulted in a lower entropy generation rate when compared with the circular and transverse elliptical cross-sectional configurations. Combining the results of the first and second law analyses for the three cross-sectional configurations, it is apparent that isotropic porous media consisting of the longitudinal elliptical cross-sectional configuration can simultaneously result in a high heat transfer efficiency and low entropy generation rate.

Effect of global plasma parameters on the transition of edge pedestal properties in [formula omitted] space

We have derived analytic expressions for the variation of the normalized pressure gradient and current density in the edge pedestal in terms of global plasma parameters. Comparison of our model with numerical results shows good agreement. Our model has been applied to explain the behavior of pedestal width and height when the plasma parameters change. The transition of the equilibrium point with the change of plasma parameters for the same pedestal width in the jϕ-α space is calculated using our model. The growth or contraction of the edge pedestal can then be determined if the new stability boundary is known.

Scaling of the toroidal structure and nonlinear dynamics of ELMs on ASDEX Upgrade

Edge localized modes (ELMs) are magnetohydrodynamic (MHD) instabilities that cause fast periodic relaxations of the strong edge pressure gradient in tokamak fusion plasmas. Magnetic pick-up coils allow the extraction of toroidal mode numbers n during the ELM cycle including the nonlinear crash on ASDEX Upgrade, providing a good comparability to nonlinear 3D MHD codes. This paper investigates how the mode numbers before and during the ELM crash change with a variation of plasma parameters. It is found that the toroidal structure size during the crash is similar to the one existing slightly before and always has a low n = 1–7 range. Furthermore, in the nonlinear phase of the ELM n does not show a clear trend with most peeling-ballooning relevant parameters such as normalized pressure gradient, bootstrap current density or triangularity, whereas a strong decrease of n with edge safety factor q95 is observed in agreement with nonlinear modeling in the here investigated high collisionality region. A simple geometric model is presented, which is capable of explaining the q scaling by existence of ballooned structures that minimize n.

Effect of the relative shift between the electron density and temperature pedestal position on the pedestal stability in JET-ILW and comparison with JET-C

The electron temperature and density pedestals tend to vary in their relative radial positions, as observed in DIII-D (Beurskens et al 2011 Phys. Plasmas 18 056120) and ASDEX Upgrade (Dunne et al 2017 Plasma Phys. Control. Fusion 59 14017). This so-called relative shift has an impact on the pedestal magnetohydrodynamic (MHD) stability and hence on the pedestal height (Osborne et al 2015 Nucl. Fusion 55 063018). The present work studies the effect of the relative shift on pedestal stability of JET ITER-like wall (JET-ILW) baseline low triangularity (δ) unseeded plasmas, and similar JET-C discharges. As shown in this paper, the increase of the pedestal relative shift is correlated with the reduction of the normalized pressure gradient, therefore playing a strong role in pedestal stability. Furthermore, JET-ILW tends to have a larger relative shift compared to JET carbon wall (JET-C), suggesting a possible role of the plasma facing materials in affecting the density profile location. Experimental results are then compared with stability analysis performed in terms of the peeling-ballooning model and with pedestal predictive model EUROPED (Saarelma et al 2017 Plasma Phys. Control. Fusion). Stability analysis is consistent with the experimental findings, showing an improvement of the pedestal stability, when the relative shift is reduced. This has been ascribed mainly to the increase of the edge bootstrap current, and to minor effects related to the increase of the pedestal pressure gradient and narrowing of the pedestal pressure width. Pedestal predictive model EUROPED shows a qualitative agreement with experiment, especially for low values of the relative shift.

On the pulsating flow behavior of a biological fluid: human blood

In this work, the rectilinear flow of a complex fluid (human blood) under a pulsating time-dependent pressure gradient is analyzed. A first approximation of the real case of blood flowing in a vein is described. The normalized pressure gradient simulates the pumping work of the heart while the flow geometry (circular tube) is assumed rigid, smooth, and cylindrical. The rheological behavior of blood with different cholesterol levels is modeled using the Bautista–Manero–Puig (BMP) constitutive equation. According to the analytical solution, a flow enhancement is predicted to first order which represents the optimum pumping work of the heart which governs the flow of blood in the entire body. This work is a contribution to the understanding of the complex rheology involved in the discontinuous pressure-driven flow of blood in the human body.

Three-Dimensional Passive and Active Control Methods of Shock Wave Train Physics in a Duct

In the present work, the physics of a three-dimensional shock train in a convergent-divergent nozzle is numerically investigated. In this regards, the Ansys-Fluent Software with Algebraic Wall-Modeled Large-Eddy Simulation (WMLES) is used. To estimate precision and errors accumulation we used the Smirinov’s method; fine flow structures are obtained via Laplacian of density called shadowgraph and the shock parameter is defined as multiplication of flow Mach number by the normalized pressure gradient, in which shock wave structures are visible distinctly. The results are compared with the experimental data of Weiss et al. [Experiments in Fluids 49(2) (2010) 355–365], in the same conditions including geometry, boundary conditions, etc. The results show that there is good agreement with experimental trends concerning wall pressure and centerline Mach number profiles. Therefore, the focus of the present study is an assessment of various flow control methods to change the shock structures. Consequently, we investigated the effects of passive (bump and cavity) and active (suction and blowing) control methods on the starting point of shock, shock strength, minimum pressure, maximum flow Mach number, etc. All CFD investigations are carried out by High Performance Computing Center (HPCC).

Aerodynamic Effects of Inclined Portals on the Initial Compression Wave Generated by a High-Speed Train Entering a Tunnel

The micropressure wave radiated from a tunnel exit is one of the environmental problems which can be investigated from the temporal pressure gradient of the compression wave. The effects of inclined portals on the initial compression wave, specifically the maximum temporal pressure gradient, are numerically studied by solving the flow field during a high-speed train nose entering a tunnel, using the unsteady three-dimensional (3D) Euler equations. After mesh independency and temporal sensitivity tests of the numerical method, validations are conducted by comparing the numerical results with experimental and numerical data. The temporal gradients of pressure wavefront are parametrically investigated for different combinations among the train speed, the blockage ratio of the train to tunnel, and inclination angle of the tunnel entrance. The numerical results show a negligible influence of train Mach number or blockage ratio on the normalized pressure gradient and noticeable effects of inclination angle, location of the train with respect to the median line of a double-tracked tunnel (DT), and the profile of train nose. Based on the numerical results, an empirical formula is proposed to predict the relationship between the maximum pressure gradient and the inclination angle of tunnel entrance.

Transient electro-osmotic and pressure driven flows of two-layer fluids through a slit microchannel

By method of the Laplace transform, this article presents semi-analytical solutions for transient electroosmotic and pressure-driven flows (EOF/PDF) of two-layer fluids between microparallel plates. The linearized Poisson-Boltzmann equation and the Cauchy momentum equation have been solved in this article. At the interface, the Maxwell stress is included as the boundary condition. By numerical computations of the inverse Laplace transform, the effects of dielectric constant ratio ɛ, density ratio ρ, pressure ratio p, viscosity ratio µ of layer II to layer I, interface zeta potential difference \(\Delta \bar \psi\), interface charge density jump Q, the ratios of maximum electro-osmotic velocity to pressure velocity α, and the normalized pressure gradient B on transient velocity amplitude are presented. We find the velocity amplitude becomes large with the interface zeta potential difference and becomes small with the increase of the viscosity. The velocity will be large with the increases of dielectric constant ratio; the density ratio almost does not influence the EOF velocity. Larger interface charge density jump leads to a strong jump of velocity at the interface. Additionally, the effects of the thickness of fluid layers (h1 and h2) and pressure gradient on the velocity are also investigated.